Fluctuations of the superconducting order parameter may strongly modify the ground state and transport properties of superconducting nanowires giving rise to qualitatively new phenomena in such systems. At low temperatures the most relevant fluctuations are coherent quantum phase slips (QPS) [1].

In superconducting nanorings such quantum phase slips (i) reduce the magnitude of superconducting persistent current (SPC) which becomes exponentially small at ring perimeters L exceeding some fundamental length and (ii) modify the periodic flux dependence of SPC from the saw-tooth form to the sinusoidal one. In this talk I will demonstrate that QPS can also induce the SPC noise [2] which can be tuned by an external magnetic flux piercing the ring.

Furthermore, quantum phase slips may generate non-equilibrium voltage fluctuations in superconducting nanowires. Employing Keldysh technique and making use of the phase-charge duality arguments we develop a theory of QPS-induced noise in such nanowires [3]. We demonstrate that quantum tunneling of the magnetic flux quanta across the wire yields quantum shot noise which obeys Poisson statistics and is characterized by a power law dependence of its spectrum SΩ on the external bias. In the low frequency limit we evaluate all cumulants of the voltage operator. Also we analyze shot noise in long wires, where SΩ decreases with increasing frequency Ω and vanishes beyond a threshold value of Ω at T→0. Quantum coherent nature of QPS noise yields non-monotonous dependence of SΩ on T at small Ω. Our predictions can be directly tested in future experiments with superconducting nanowires and nanorings.